1)ABCD is a cyclic quadrilateral. If <ACD = 40°, <ADC = 80°. Find <CBD
2) If the ratio of the radius of two cylinder of same height is 3/4. Find the ratio of their volume
Answers
1) Given:-
- ABCD is a cyclic quadrilateral.
To Find:-
Note:-
Refer to the attachment provided for a better idea of the scene.
Solution:-
In quad.ABCD,
We know,
The opposite angles of a cyclic quadrilateral are supplementary.
Hence,
=
=
=
Now,
We also know,
Angles on the same segment of a cyclic quadrilateral are always equal.
Hence,
=>
Now,
=
=
=
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2. Given:-
- Ratio of radius of two cylinders = 3:4
- Height of both the cylinders are same.
To Find:-
Ratio of volume of the two cylinders.
Assumption:-
Let the radius of 1st cylinder be and the radius of 2nd cylinder be
Let the height of both the cylinders be h.
Solution:-
We know,
Volume of a cylinder = πr²h
Therefore for 1st cylinder,
=
=
Now,
For the 2nd cylinder,
=
=
Now,
Ratio of the Volumes of both the cylinder =
=
=
=
=
=
Therefore the ratio of volumes of both the cylinders is 9:16.
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Let us f1st recall the properties of cyclic quadrilateral. In a cyclic quadrilateral sum of opp. angles is 180° and in a Circle angles made from the same segments are equal.
Here,
Substitute this value:-
Now,
Substituting these values:-
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Let, Radius of 1st cylinder be 'R' = 3
Radius of 2nd Cylinder be 'r' = 4
Height of both cylinder is 'h'
Now, using
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